Lauer had been promised the first interview live on Jan. 19. But the day before, Sullenberger's pilots association asked him to postpone interviews while the investigation into U.S. Airways Flight 1549 and its water landing continued.
Sullenberger was praised as a hero for a deft landing on Jan. 15, after both of the plane's engines were disabled following a collision with a flock of birds. All 155 passengers and crew members were rescued.
Despite the postponement, NBC's "Today" said it had a continued commitment with Sullenberger's family and media adviser to have the first interview.
"What Captain Sullenberger did in the cockpit on Flight 1549 was heroic and admirable," said NBC News spokeswoman Megan Kopf. "Unfortunately, people close to him have not acted nearly as admirably over the past few days. They gave us their word, and then broke their commitment. We wish Captain Sullenberger the best."
The "Today" show has no plans now to interview Sullenberger.
The Sullenbergers' media adviser, Alex Clemens of the communications firm Barbary Coast Consulting, confirmed the "60 Minutes" interview but said he would have no other comment.
If it came down to considering whether television's leading prime-time newsmagazine has more juice for publicity than TV's leading morning show, "60 Minutes" typically gets more viewers with the potential for grabbing a particularly large audience for newsmaking interviews.